The function f(x)=a sin x+1/3x has maximum value at x =π/3. The value of a is

The portion of the tangent drawn at any point on x^2/3+y^2/3=a^2/3 (a>0), except the points on the coordinate axes, included between the coordinate axes is

The length of the tangent of the curve 2x²+3xy-2y²=8 at (2, 3) is

The stationary point of f(x)=2x³-9x²+12x-3 is

The length of the sub tangent   of the curve y²=x³/2a-x at (a, a) is

The length of the sub normal to the curve y²=4ax at any point

The point on the curve x²+y²-2x-3=0 at which the tangent is parallel to x-axis is

The equation of the tangent to the curve 2x²-xy+3y2=18 at (3, 1) is

If there is an error of 0.02 cm in the measurement of the side 10 cm of a cube, then error in the surface area is

The side of an equilateral triangle increases at the uniform rate 0.05 cm/sec. the rate of increase in the area of the triangle when the side is 20 cm is